Endogenous quasicycles and stochastic coherence in a closed endemic model

Bacterial growth: a statistical physicist's guide

Bacterial growth presents many beautiful phenomena that pose new theoretical challenges to statistical physicists, and are also amenable to laboratory experimentation. This review provides some of the essential biological background, discusses recent applications of statistical physics in this field, and highlights the potential for future research.

Delay-managed tradeoff in the molecular dynamics of the segmentation clock

The molecular segmentation clock is a complex regulatory network that governs the periodic somite segmentation in vertebrate embryos. Underlying the rhythm of the segmentation clock is a single-cell level pace-making circuit, where inevitable molecular noise and time delay impose normal operating constraints to the pace-making. However, how the molecular mechanisms of the core circuit of the segmentation clock coordinate the operating constraints and maintain the rhythmic nature of the developmental process remains poorly understood. To address this question, we construct two biologically-motivated mathematical models with multiple clock protein transcription binding sites, with differential or rate-limited decay rates for protein monomers and dimers. We demonstrate that the rate-limited decay significantly enlarges the parameter space of noise-induced and delay-induced oscillations. Interestingly, focusing on the stochastic characters of noise-induced and delay-induced oscillations in terms of phase coherence and phase averaged amplitude noise in the polar coordinate, we find that there is a delay-managed tradeoff between phase coherence and phase averaged amplitude noise. In particular, the model with both multiple binding sites and rate-limited decay can show regular tunability as the delay increases. Our results indicate that transcriptional and post-translational mechanisms constrain the combined effects of noise and delay on the molecular dynamics of the segmentation clock.

Oscillating microbial dynamics driven by small populations, limited nutrient supply and high death rates

Predicting and controlling the behaviour of microbial ecosystems demands a fundamental understanding of the factors controlling their dynamics. In the natural environment microbes typically live in small local populations with limited and unpredictable nutrient supply and high death rates. Here, we show that these conditions can produce oscillations in microbial population dynamics, even for a single population. For a large population, with deterministic growth dynamics, our model predicts transient (damped) oscillations. For a small population, demographic noise causes these oscillations to be sustained indefinitely. We show that the same mechanism can produce sustained stochastic oscillations in a two-species, nutrient-cycling microbial ecosystem. Our results suggest that oscillatory population dynamics may be a common feature of small microbial populations in the natural environment, even in the absence of complex interspecies interactions or spatial structuring.

Phase lag in epidemics on a network of cities

We study the synchronization and phase lag of fluctuations in the number of infected individuals in a network of cities between which individuals commute. The frequency and amplitude of these oscillations is known to be very well captured by the van Kampen system-size expansion, and we use this approximation to compute the complex coherence function that describes their correlation. We find that, if the infection rate differs from city to city and the coupling between them is not too strong, these oscillations are synchronized with a well-defined phase lag between cities. The analytic description of the effect is shown to be in good agreement with the results of stochastic simulations for realistic population sizes.